DESCRIPTION (Applicant's abstract): The long-term goal of this proposal is to determine efficient and ethically attractive designs for phase I clinical trials, determine appropriate estimation procedures for the maximum tolerated dose (MTD), and to impact practice by providing state-of-the art design software for use by investigators. Background: Phase I clinical trials are typically very small, uncontrolled, sequential studies of human subjects designed to determine the maximum tolerate dose of an experimental drug. Perhaps because phase I clinical trials are generally non- randomized, do not involve large samples, and are not hypothesis-driven, statistical considerations have often been ignored. However, trials that do not accurately find the correct MTD may result in inadequate dose levels (from the standpoint oi effectiveness) being passed on to further testing or in highly toxic dose levels being passed on to later phase trials. "Conventional" designs have been popular for some time, where patients are treated in groups of three, and doses are escalated or de-escalated depending on their responses. Such methods simply identify an MTD as a function of the data, and hence estimation is not relevant. Others have taken a more formal approach, by treating the MTD as an unknown parameter of a dose-response curve. The problem then becomes one of quantile estimation. This is the approach we take in this proposal. Parametric Bayesian methods (e.g., continual reassessment method; escalation with overdose control) and nonparametric methods (e.g., random walk rules) have been proposed as designs that allow efficient estimation of a quantile of interest. Specific Aim I derives the Bayesian optimal design for estimation of a quantile under a constraint that the assigned dose levels do not exceed a specified quantile. We extend this problem into a Bayesian sequential design, under the same constraint, in specific Aim II. Specific Aim III extends Specific Aims I and 11 by dealing with non-binary ordinal responses from the WHO toxicity scale. We propose to use a proportional odds model to derive the constrained Bayesian optimal design and its sequential analog. Specific Aim IV proposes to use a random walk rule to develop a nonparametric design for a trial with ordinal toxicity scale. We will explore appropriate estimation procedures in Specific Aim V. In Specific Aim VI, we intend to do a formal comparison of existing methodology for phase I clinical trials with the methodology developed in Specific Aims I-V. We intend to use state-of-the-art computational facilities to find exact distributions of ethical parameters of interest. Finally, we develop user-friendly front-end software to facilitate the conduct of phase I clinical trials in Specific Aim VII.